Prove polynomial identities and use them to solve or describe numerical relationships.
Factor an expression using a polynomial identity
Problem
Factor \(x^2~-~9\) completely using a polynomial identity.
Big Picture
What this problem is really about
Identify the identity from the expression’s visible structure before doing any algebra. Count the terms, note whether they are added or subtracted, and rewrite each as an exact square or cube. For a two-term difference of squares, use the square roots in opposite-sign factors, then multiply back to confirm that no middle term remains.
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